w(3w+2)-2(w^2-8)=w(w+5)-6w+7

Solution for w(3w+2)-2(w^2-8)=w(w+5)-6w+7 equation:

Simplifying
w(3w + 2) + -2(w2 + -8) = w(w + 5) + -6w + 7

Reorder the terms:
w(2 + 3w) + -2(w2 + -8) = w(w + 5) + -6w + 7
(2 * w + 3w * w) + -2(w2 + -8) = w(w + 5) + -6w + 7
(2w + 3w2) + -2(w2 + -8) = w(w + 5) + -6w + 7

Reorder the terms:
2w + 3w2 + -2(-8 + w2) = w(w + 5) + -6w + 7
2w + 3w2 + (-8 * -2 + w2 * -2) = w(w + 5) + -6w + 7
2w + 3w2 + (16 + -2w2) = w(w + 5) + -6w + 7

Reorder the terms:
16 + 2w + 3w2 + -2w2 = w(w + 5) + -6w + 7

Combine like terms: 3w2 + -2w2 = 1w2
16 + 2w + 1w2 = w(w + 5) + -6w + 7

Reorder the terms:
16 + 2w + 1w2 = w(5 + w) + -6w + 7
16 + 2w + 1w2 = (5 * w + w * w) + -6w + 7
16 + 2w + 1w2 = (5w + w2) + -6w + 7

Reorder the terms:
16 + 2w + 1w2 = 7 + 5w + -6w + w2

Combine like terms: 5w + -6w = -1w
16 + 2w + 1w2 = 7 + -1w + w2

Solving
16 + 2w + 1w2 = 7 + -1w + w2

Solving for variable 'w'.

Reorder the terms:
16 + -7 + 2w + w + 1w2 + -1w2 = 7 + -1w + w2 + -7 + w + -1w2

Combine like terms: 16 + -7 = 9
9 + 2w + w + 1w2 + -1w2 = 7 + -1w + w2 + -7 + w + -1w2

Combine like terms: 2w + w = 3w
9 + 3w + 1w2 + -1w2 = 7 + -1w + w2 + -7 + w + -1w2

Combine like terms: 1w2 + -1w2 = 0
9 + 3w + 0 = 7 + -1w + w2 + -7 + w + -1w2
9 + 3w = 7 + -1w + w2 + -7 + w + -1w2

Reorder the terms:
9 + 3w = 7 + -7 + -1w + w + w2 + -1w2

Combine like terms: 7 + -7 = 0
9 + 3w = 0 + -1w + w + w2 + -1w2
9 + 3w = -1w + w + w2 + -1w2

Combine like terms: -1w + w = 0
9 + 3w = 0 + w2 + -1w2
9 + 3w = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
9 + 3w = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(3 + w) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(3 + w)' equal to zero and attempt to solve:

Simplifying
3 + w = 0

Solving
3 + w = 0

Move all terms containing w to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + w = 0 + -3
w = 0 + -3

Combine like terms: 0 + -3 = -3
w = -3

Simplifying
w = -3
Solution
w = {-3}